The California Highway Patrol said the agency's helicopter first witnessed the suspect's Infiniti car doing "donuts" at a street takeover, and officers later found the child in the back seat, along with a nitrous oxide tank, balloons and a bottle of alcohol inside the car.
Authorities said an investigation determined the infant was still in the car when the driver was doing the spins.
CHP posted a photo on social media showing the child in a car seat and wrapped in a blue and white blanket. A Hennessy bottle that appeared to contain alcohol and the tank were also pictured.
The driver was arrested on suspicion of felony child endangerment, reckless driving and exhibition of speed, CHP said.
Authorities said the child, who was not injured, was taken to their mother and Child Protective Services was contacted.